The Strong Decays of Orbitally Excited $B_{sJ}^{\ast }$ Mesons by Improved Bethe-Salpeter Method

We calculate the masses and the strong decays of orbitally excited states $B_{s0}$, $B_{s1}^{\mathrm{\prime }}$, $B_{s1}$ and $B_{s2}$ by the improved Bethe-Salpeter method. The predicted masses of $B_{s0}$ and $B_{s1}^{\mathrm{\prime }}$ are $M_{B_{s0}}=5.723\pm 0.280\mathrm{G}\mathrm{e}\mathrm{V}$, $M_{B_{s1}^{\mathrm{\prime }}}=5.774\pm 0.330\mathrm{G}\mathrm{e}\mathrm{V}$. We calculate the isospin symmetry violating decay processes $B_{s0}\to B_s\pi$ and $B_{s1}^{\mathrm{\prime }}\to B_s^{\ast }\pi$ through ${\pi }^0-\eta$ mixing and get small widths. Considering the uncertainties of the masses, for $B_{s0}$ and $B_{s1}^{\mathrm{\prime }}$, we also calculate the OZI allowed decay channels: $B_{s0}\to B\bar{K}$ and $B_{s1}^{\mathrm{\prime }}\to B^{\ast }\bar{K}$. For $B_{s1}$ and $B_{s2}$, the OZI allowed decay channels $B_{s1}\to B^{\ast }\bar{K}$, $B_{s2}\to B\bar{K}$ and $B_{s2}\to B^{*}\bar K$ are studied. In all the decay channels, the reduction formula, PCAC relation and low energy theorem are used to estimate the decay widths. We also obtain the strong coupling constants $G_{B_{s0}{B}_s\pi }$, $G_{B_{s0}B\bar{K}}$, $G_{B_{s1}^{\mathrm{\prime }}{B}_s^{\ast }\pi }$, $F_{B_{s1}^{\mathrm{\prime }}{B}_s^{\ast }\pi }$, $G_{B_{s1}^{\mathrm{\prime }}{B}^{\ast }\bar{K}}$, $F_{B_{s1}^{\mathrm{\prime }}{B}^{\ast }\bar{K}}$, $G_{B_{s1}{B}^{\ast }\bar{K}}$, $F_{B_{s1}{B}^{\ast }\bar{K}}$, $G_{B_{s2}B\bar{K}}$ and $G_{B_{s2}{B}^{\ast }\bar{K}}$.